Speaker
Description
In statistical analyses of binary outcomes for medical procedures performed by multiple health care providers, provider-specific effects are commonly handled using conditional models with random effects or using marginal models with generalized estimating equations (GEEs). While convenient, these models treat provider effects primarily as nuisance parameters, even though they may themselves be of substantive interest—for example, when evaluating performance variation across providers. Moreover, the shrinkage inherent in random-effects estimation typically leads to underestimation of between-provider differences.
In this talk, we will discuss how the Firth correction could be embedded in such models. The Firth correction is a penalized-likelihood method originally introduced to reduce bias of maximum likelihood estimates which may result from high predictor dimensionality, near-multicollinearity, and sparse outcome events. An extreme form of this bias is separation, caused, e.g., if no events are observed at one level of a categorical predictor variable. Separation leads to non-existence of the maximum likelihood solution, but can be entirely prevented by the Firth correction. This attractive property may have contributed to that method's high popularity. Unlike other penalized-likelihood methods, the Firth correction does not have a tuning parameter. However, a well-known limitation of the Firth correction is its tendency to shrink predicted probabilities toward 0.5. To mitigate this, two straightforward modifications—FLIC and FLAC—have been proposed and will be reviewed in this talk.
In provider-specific models, the Firth correction may be considered (i) to replace mixed-effects methods by treating providers as fixed effects, or (ii) to solve a separation problem related to fixed effects of providers or other variables that perfectly explain the outcome.
For case (i) the Firth correction is expected to shrink provider effects less than mixed-effects methods. Moreover, it is transformation-invariant and does not require any distributional assumptions on the provider effects. However, its attractive bias-correcting property theoretically only holds if the number of subjects per health care provider is not too small. For case (ii) extensions of GEEs and mixed effects logistic regression models incorporating the Firth correction were recently proposed to mitigate separation problems. For mixed models, these novel methods can simultaneously deal with convergence issues caused by either random or fixed effects. We will give an overview over these recent developments.
Finally, we will provide some illustrative analyses of data examples to compare the operation characteristics of these models in health care provider-specific applications.
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